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Simplifying 3(6z + -1) + -4(z + 4) = 12(z + 1) Reorder the terms: 3(-1 + 6z) + -4(z + 4) = 12(z + 1) (-1 * 3 + 6z * 3) + -4(z + 4) = 12(z + 1) (-3 + 18z) + -4(z + 4) = 12(z + 1) Reorder the terms: -3 + 18z + -4(4 + z) = 12(z + 1) -3 + 18z + (4 * -4 + z * -4) = 12(z + 1) -3 + 18z + (-16 + -4z) = 12(z + 1) Reorder the terms: -3 + -16 + 18z + -4z = 12(z + 1) Combine like terms: -3 + -16 = -19 -19 + 18z + -4z = 12(z + 1) Combine like terms: 18z + -4z = 14z -19 + 14z = 12(z + 1) Reorder the terms: -19 + 14z = 12(1 + z) -19 + 14z = (1 * 12 + z * 12) -19 + 14z = (12 + 12z) Solving -19 + 14z = 12 + 12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-12z' to each side of the equation. -19 + 14z + -12z = 12 + 12z + -12z Combine like terms: 14z + -12z = 2z -19 + 2z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -19 + 2z = 12 + 0 -19 + 2z = 12 Add '19' to each side of the equation. -19 + 19 + 2z = 12 + 19 Combine like terms: -19 + 19 = 0 0 + 2z = 12 + 19 2z = 12 + 19 Combine like terms: 12 + 19 = 31 2z = 31 Divide each side by '2'. z = 15.5 Simplifying z = 15.5
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